Controloriented Modelling and Identification: Theory and practice
This comprehensive book covers the stateoftheart in controloriented modelling and identification techniques. With contributions from leading researchers in the subject, Controloriented Modelling and Identification: Theory and practice covers the main methods and tools available to develop advanced mathematical models suitable for control system design, including: objectoriented modelling and simulation; projectionbased model reduction techniques; integrated modelling and parameter estimation; identification for robust control of complex systems; subspacebased multistep predictors for predictive control; closedloop subspace predictive control; structured nonlinear system identification; and linear fractional LPV model identification from local experiments using an H1based glocal approach. This book also takes a practical look at a variety of applications of advanced modelling and identification techniques covering spacecraft dynamics, vibration control, rotorcrafts, models of anaerobic digestion, a brakebywire racing motorcycle actuator, and robotic arms.
Inspec keywords: predictive control; aircraft control; reduced order systems; helicopters; actuators; largescale systems; closed loop systems; control system synthesis; nonlinear control systems; manipulators; motorcycles; robust control; linear parameter varying systems; parameter estimation
Other keywords: vibration control; control system design; structured nonlinear system identification; mathematical model; controloriented modelling; identification technique; robust control; complex systems; subspacebased multistep predictor; linear fractional LPV model identification; objectoriented modelling and simulation; projectionbased model reduction technique; anaerobic digestion; brakebywire racing motorcycle actuator; spacecraft dynamics; integrated modelling; closedloop subspace predictive control; rotorcraft; parameter estimation; robotic arm
Subjects: Control system analysis and synthesis methods; Manipulators; General and management topics; Specific control systems; Actuating and final control devices; Transportation system control; Optimal control; Simulation, modelling and identification
 Book DOI: 10.1049/PBCE080E
 Chapter DOI: 10.1049/PBCE080E
 ISBN: 9781849196147
 eISBN: 9781849196154
 Format: PDF

Front Matter
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1 Introduction to controloriented modelling
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The process of developing controloriented mathematical models of physical systems is a complex task, which in general implies a careful combination of prior knowledge about the physics of the system under study and information coming from experimental data. The aim of this book is to present stateoftheart methods and tools available within the systems and control literature to support controloriented modelling activities and to illustrate their usefulness by means of a number of case studies and applications.

2 Objectoriented modelling and simulation of physical systems
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Modular dynamic models based on physical first principles are often an essential part of the control system design and performance verification process. Traditional block diagrams, which are popular among control engineers, are not an appropriate modelling paradigm in this context, because they assume causal connections, while physical connections are acausal in nature. This chapter introduces the basic concepts of equationbased, objectoriented (OO) modelling and simulation of physical system, with specific reference to the Modelica language. The key ideas and algorithms for the mathematical processing of OO models are then outlined. Finally, the application of OO modelling to various phases of the control system design process is illustrated.

3 Projectionbased model reduction techniques
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This chapter is aimed at providing, from the authors point of view, the most representative techniques of linear timeinvariant (LTI) model approximation. For an exhaustive overview of all the existing model approximation methods, the reader should refer to [3] and references therein. With this in mind, two sets of methods are presented: truncation methods, and especially the balanced one and Krylov, or moment matching methods. Balanced truncation is grounded on the singular value decomposition (SVD) and is often considered as the gold standard of model reduction. Its standard form as well as its frequencylimited counterpart is presented. The moment matching methods are aimed at interpolating the initial model and its derivatives at some points through projection on some specific Krylov subspaces. These approaches have known significant development in the past few years. Both truncation methods and moment matching methods can be brought together under the underlying framework of approximation by projection. There exist other approaches which are not based on projection but rather on optimization procedures. Since the theoretical framework is quite different, they are not presented in this chapter and the reader should refer to [4, 21] or [31] for further details.

4 Integrated modelling and parameter estimation: an LFR  Modelica approach
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Linear fractional representations (LFRs) are a widely used model description formalism in modern control and system identification theory. Deriving such models from physical first principles is a nontrivial and often tedious and errorprone process, if carried out manually. Tools already exist to transform symbolic transfer functions and symbolic statespace representations into reducedorder LFRs, but these descriptions are still quite far from a natural, physicalbased, objectoriented description of physical and technological systems and are moreover hard to integrate with model identification tools. In this chapter a new approach to LFR modelling and identification starting from equationbased, objectoriented descriptions of the plant dynamics (formulated using the Modelica language) and inputoutput data is presented. This approach allows to reduce the gap between userfriendly model representations, based on object diagrams with physical connections, block diagrams with signal connections, and generic differentialalgebraic models, and the use of advanced LFRbased identification and control techniques.

5 Identification for robust control of complex systems: algorithm and motion application
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Increasing performance demands in control applications necessitate accurate modeling of complex systems for control. The aim of this chapter is to develop a new system identification algorithm that delivers models that are suitable for subsequent robust control design and can be reliably applied to complex systems. To achieve this, an identification algorithm is developed that delivers a system model in terms of recently developed coprime factorizations and thereby extends classical iterative procedures to the closedloop case. These coprime factorizations have important advantages for uncertainty modeling and robust controller synthesis of complex systems. A numerically optimal implementation is presented that relies on orthonormal polynomials with respect to a datadependent discrete inner product. Experimental results on a nanometeraccurate positioning system confirm that the algorithm is capable of delivering the required coprime factorizations and the implementation is numerically reliable, which is essential for complex systems as common implementations suffer from severe illconditioning.

6 Subspacebased multistep predictors for predictive control
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In the framework of the subspacebased identification of linear systems, the first step for the construction of a statespace model from observed inputoutput data involves the estimation of the output predictor. Such construction is based on projection operations of certain structured data matrices onto suitable subspaces spanned by the collected data. To the purpose of predictive control using shortterm predictors, this algorithmic step can be elaborated to provide databased multistep predictors. Using such an approach, this contribution deals with subspacebased identification methods for the estimation of shortterm predictors. One illustrative example is provided: blood glucose prediction in type 1 diabetes mellitus.

7 Closedloop subspace predictive control
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This chapter considers subspace predictive control of systems whose dynamics can be described locally by LTI models. The control algorithm is based on the predictorbased subspace identification framework. In a linear leastsquares problem, the observer Markov parameters of the system are recursively estimated. Those parameters are used to construct an output predictor which is in turn used to solve a predictive control problem subject to constraints.

8 Structured nonlinear system identification
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To obtain an identified model from data, the system identification practitioner has to make an important choice: to specify the set of candidate models, or model structure. This choice can play an outsized role on the success or failure of the identification process. If the model structure is specified too restrictively, so that the true system is not represented, then the identified model will be biased. On the other hand, if the model structure is specified too generally, then the identified model can have a high variance, and a significant amount of data may be needed to reduce the sensitivity to measurement noise. Ideally, the practitioner should choose the model structure so that it encodes all the information that is known with high confidence. The structured nonlinear system identification approach is designed to give the practitioner a very flexible model structure that can easily be configured to be as restrictive or permissive as the apriori information about the system warrants. In this chapter, a complete introduction to structured identification is developed, with examples relevant to many different realworld applications integrated throughout.

9 Linear fractional LPV model identification from local experiments using an H∞based glocal approach
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In this chapter a new identification technique is introduced to estimate a linear fractional representation (LFR) of a linear parametervarying (LPV) system from local experiments using a dedicated nonsmooth optimization procedure. Having access to a reliable set of local models, this technique consists more specifically in optimizing an H_{∞}normbased cost function measuring the fit between the local information (represented by the locally estimated LTI models) and the local behavior of a parameterized global LPV model. The method presented in this chapter results directly in an LPV model whose parametric matrices can be rational functions of the scheduling variables without any interpolation step (required usually by the local approach) and without writing the local fully parameterized LTI statespace models with respect to a coherent basis. On top of that, specific attention is paid to parameterized LPV models satisfying a fully parameterized or a physically structured linear fractional representation. This identification procedure is tested and validated with a simulation example.

10 Objectoriented modelling of spacecraft dynamics: tools and case studies
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The development process for spacecraft control systems relies heavily on modelling and simulation tools for spacecraft dynamics. For this reason, there is a strong need for adequate design tools in order to cope efficiently with tight budget and time constraints for space missions. In this chapter the main issues related to the modelling and simulation of satellite dynamics for control purposes are first discussed and an objectoriented modelling framework, implemented as a Modelica library, is then presented. The proposed tools enable a unified approach to a range of problems spanning from initial mission design and actuator sizing phases, down to detailed closedloop simulation of the control system, including realistic models of sensors and actuators. It also promotes the reuse of modelling knowledge among similar missions, thus minimizing the design effort for any new project. The proposed framework and the Modelica library are demonstrated by means of two case studies.

11 Controloriented aeroelastic BizJet loworder LFT modeling
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To accelerate aircraft conception and reduce development costs, computeraided preliminary design is widely used (e.g., for controller design, performance analysis etc.). The computerbased approach has been rendered possible thanks to advances in modeling tools, allowing to faithfully reproduce complex physical phenomena with limited  expensive  experimental tests. Due to these economical considerations and technological advances, aeronautical control engineers can rely and work with a considerable amount of very accurate models. The counterpart of this accuracy is the resulting numerical complexity which leads (i) to a prohibitively large number of variables to manage, rendering the control design task very complex (i.e., numerical tools become nearly inefficient), and (ii) to models with an accuracy level too high for the control synthesis purpose (indeed modern control techniques usually require loworder representations). In this chapter, based on multiple initial largescale linear time invariant models, the problem of constructing a suitable loworder parameter dependent model, appropriate to the control design purpose, is addressed. The proposed solution is illustrated on a complex generic Business Jet (BizJet) aeroelastic controldesign problem.

12 Active vibration control using subspace predictive control
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In this chapter we apply the subspace predictive control algorithm to the problem of active vibration control of a flexible beam. The flexible beam is equipped with piezoelectric transducers. This example application demonstrates that computations can be performed in real time for a realistic system and it shows how the scheme rapidly adapts when a sudden significant change in structural dynamics is introduced by changing one of the structural parameters.

13 Rotorcraft system identification: an integrated time  frequencydomain approach
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The problem of rotorcraft system identification is considered and a novel, twostep technique is proposed, which combines the advantages of timedomain and frequencydomain methods. In the first step, the identification of a blackbox model using a subspace model identification method is carried out, using a technique which can deal with data generated under feedback; subsequently, in the second step, apriori information on the model structure is enforced in the identified model using an H_{∞} model matching method. A bootstrapbased approach is used to estimate model uncertainty for the identified models. A simulation study is used to illustrate the proposed approach.

14 Parameter identification of a reduced order LFT model of anaerobic digestion
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Owing to their complexity, accurate and detailed models of anaerobic digestion cannot be used for online monitoring and control. To this aim reduced order models have to be considered. In this chapter, a modification of the wellknown AMOCO model is first proposed in order to widen its field of applicability. Then, to perform parameter identification, a linear fractional transformation (LFT) formulation is derived, thanks to the use of a symbolic manipulation tool applied to an objectoriented model formulation. The approach has been applied to two case tests: in the first test, the data used for identification have been generated by a simulation of the fully detailed Anaerobic Digestion Model no. 1 (ADM1) model, assuming waste activated sludge as influent substrate, and in the second, the data have been collected on a real plant, used for anaerobic digestion of agricultural wastes.

15 Modeling and parameter identification of a brakebywire actuator for racing motorcycles
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This chapter presents a controloriented model of an electrohydraulic brakebywire actuator for racing motorcycles. Starting from a detailed description of the device, a firstprinciple model is derived. The model parameters are identified following a graybox approach. Experimental results are used to validate the model and carry out a parameter sensitivity analysis.

16 LPV modeling and identification of a 2DOF flexible robotic arm from local experiments using an H∞based glocal approach
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This chapter presents a series of methodological contributions for the identification of flexible manipulators from experimental data. The goal of this identification procedure consists more precisely in obtaining reliable LPV models written as linearfractional representations (LFR) for a 2DOF robotic manipulator having structural flexibilities. The case of a twosegment arm initially designed for cardiac robotized surgery is more specifically considered in simulation. In order to reach this goal, the H_{∞}based optimization technique described in Chapter 9 is applied. This methodology is indeed very flexible and allows us to derive models with or without structure. Thus, as far as the model structure is concerned, two different cases are considered in this chapter. First, a specific attention is paid to a fully parameterized LPVLFR, the parameters of which are estimated on the gathered I/O data sequences exclusively. Second, the prior information derived from the study of the nonlinear equations governing the behavior of the robotic manipulator is used to build the structure of the LPVLFR and an LPV physically structured statespace form is identified from the same I/O data sequences as those used for the fully parameterized statespace form. This study proves that using the synergy between an analytic and an experimental approach can be really helpful for the identification of an LPV flexible robotic manipulator model.

Back Matter
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